arXiv subjects

Karol Gietka

Publications and source records attributed to Karol Gietka.

At least 19 recordsLinked to original sources

arXiv2026

Simulating cavity QED with spin-orbit coupled Bose-Einstein condensates revisited

Simulating cavity quantum electrodynamics in synthetic platforms offers a promising route to exploring light-matter interactions without real photons, while enabling the transfer of cavity-based techniques to other systems. Among such platforms, Bose-Einstein condensates with synthetic spin-orbit coupling provide a controllable setting where internal and motional degrees of freedom become coupled, mimicking aspects of cavity quantum electrodynamics. In this work, we critically assess the extent to which spin-orbit coupled Bose-Einstein condensates can emulate cavity quantum electrodynamics phenomena, with a focus on squeezing and entanglement generation. We show that spin-orbit coupled Bose-Einstein condensates can faithfully reproduce the physics of a single atom coupled to a quantized field, realizing an analogue of the quantum Rabi model but inherently fail to capture genuine collective effects characteristic of the Dicke model, such as cavity-mediated many-body entanglement. Our results clarify both the potential and the fundamental limitations of spin-orbit coupled Bose-Einstein condensates as analogue quantum simulators of cavity quantum electrodynamics, offering guidance for future strategies to generate and control non-classical states of matter in photon-free, highly tunable platforms.

cond-mat.quant-gas↗

arXiv2026

Mind the Gap: Anti-Critical Quantum Metrology

Critical quantum metrology exploits the dramatic growth of the quantum Fisher information near quantum phase transitions to enhance the precision of parameter estimation. This enhancement is commonly associated with a closing energy gap, which causes the characteristic timescales for adiabatic preparation or relaxation to diverge with increasing system size. As a consequence, the apparent growth of the quantum Fisher information largely reflects the increasing evolution time induced by critical slowing down rather than a genuine improvement in metrological performance, thereby limiting the practical usefulness of such protocols. Here we show that the relationship between energy gaps, quantum correlations, and achievable precision in interacting quantum systems can be far more subtle. In particular, quantum-enhanced sensitivity can also emerge when the energy gap increases, eliminating critical slowing down and enabling substantially faster relaxation dynamics. Although the corresponding quantum Fisher information may decrease due to the shorter evolution time, the resulting precision can nevertheless remain quantum-enhanced. Building on this insight, we introduce an anti-critical quantum metrology scheme in which quantum-enhanced precision arises while the energy gap grows. We illustrate this mechanism using the quantum Rabi model, thereby identifying a route to metrological advantage that avoids the slow dynamics associated with conventional criticality.

quant-ph↗

arXiv2025

Frequency shifts heralding ground state squeezing and entanglement of two coupled harmonic oscillators

It is often argued that two linearly coupled quantum harmonic oscillators, even when cooled to their ground state, display no inherently quantum features beyond quantized energy levels. Here, we challenge this view by showing that their classical observables encode genuinely quantum features. In particular, we demonstrate that the characteristic frequency shifts observed in coupled oscillators signal non-classical correlations and ground-state entanglement at zero temperature corresponding to two-mode squeezing between the uncoupled modes. From a complementary perspective, these two effects, frequency shifts and squeezing, represent the same underlying phenomenon but expressed in different mode bases. What appears as a spectral renormalization in one description manifests itself as entanglement in the other. Frequency shifts therefore constitute an entanglement witness accessible via standard spectroscopy. While the underlying squeezing is not directly measurable, it can be exploited to enhance the signal-to-noise ratio in precision frequency measurements of individual oscillators without requiring squeezed quantum noise. This uncovers a new route to quantum-enhanced sensing within systems traditionally regarded as classical, offering fresh insight into how signatures of quantumness persists across the quantum-to-classical boundary.

quant-ph↗

arXiv2025

Critical Quantum Sensing: a tutorial on parameter estimation near quantum phase transitions

Quantum phenomena offer the possibility of measuring physical quantities with precision beyond classical limits. However, current progress is constrained by scalability, environmental noise, and challenges in practical integration. This highlights the necessity for novel approaches. An emerging paradigm in this direction is critical quantum metrology -- which harnesses the enhanced susceptibility and nonclassical correlations naturally occurring near quantum phase transitions as resources for quantum-enhanced precision. This tutorial provides a pedagogical introduction to key concepts and a detailed overview of prominent quantum sensing strategies that exploit critical phenomena in metrology. Through examples of increasing complexity, the reader is guided through various critical quantum sensing protocols applied to different critical systems. Special emphasis is placed on the optimal scaling of estimation precision with respect to fundamental resources. Finally, we discuss how critical quantum metrology extends from idealized models to realistic open-system, dissipative regimes, and strongly correlated fermionic systems, outlining both the challenges and opportunities for future quantum technologies.

quant-ph↗

arXiv2025

Quantum Metrology in the Ultrastrong Coupling Regime of Light-Matter Interactions: Leveraging Virtual Excitations without Extracting Them

Virtual excitations, inherent to ultrastrongly coupled light-matter systems, induce measurable modifications in system properties, offering a novel resource for quantum technologies. In this work, we demonstrate how these virtual excitations and their correlations can be harnessed to enhance precision measurements, without the need to extract them. Building on the paradigmatic Dicke model, which describes the interaction between an ensemble of two-level atoms and a single radiation mode, we propose a method to harness hybridized light-matter modes whose renormalized frequencies encode the effects of virtual excitations for quantum metrology. Remarkably, we find that for a fixed squeezing parameter $ξ$, exploiting virtual squeezing through oscillator frequency shifts yields a quadratic enhancement in estimation precision -- scaling as $\exp(4ξ)$ -- compared to the conventional $\exp(2ξ)$ scaling of real squeezed states. These results show that virtual excitations, though unobservable, can drive metrological performance beyond the standard quantum limit. Our approach establishes a broadly applicable framework for high-precision measurements across a wide class of ultrastrongly coupled quantum systems.

quant-ph↗

arXiv2025

Conditional Entanglement Amplification via Non-Hermitian Superradiant Dynamics

Due to the inherently probabilistic nature of quantum mechanics, each experimental realization of a dynamical quantum system may yield a different measurement outcome, especially when the system is coupled to an environment that causes dissipation. Although it is in principle possible that some quantum trajectories lead to exotic highly entangled quantum states, the probability of observing these trajectories is usually extremely low. In this work, we show how to maximize the probability of generating highly entangled states, including maximally entangled cat states, in an ensemble of atoms experiencing superradiant decay. To this end, we analyze an effective non-Hermitian Hamiltonian which governs the dynamics between the quantum jumps associated with photon emission. A key result of our study is that, in order to maximally enhance the probability of cat state generation, the initial state needs to be non-classical. This can be achieved e.g. with one-axis twisting in a cavity-QED system.

quant-ph↗

arXiv2025

Uncertain Quantum Critical Metrology: From Single to Multi Parameter Sensing

Critical quantum metrology relies on the extreme sensitivity of a system's eigenstates near the critical point of a quantum phase transition to Hamiltonian perturbations. This means that these eigenstates are extremely sensitive to all the parameters of the Hamiltonian. In realistic settings, there is always some degree of uncertainty in the control parameters used to tune the system to criticality. These uncertainties, while not the target of estimation, can significantly affect the attainable precision, effectively acting as nuisance parameters in the estimation process. Despite being a practically relevant source of noise, their impact on critical metrology has been largely overlooked. In this work we present a general framework that interpolates between single- and multiparameter estimation settings, enabling a systematic analysis of how such uncertainties influence sensitivity. We apply this framework to the paradigmatic transverse field Ising and Lipkin-Meshkov-Glick models, explicitly demonstrating how uncertainty in control parameters affects the metrological performance of critical sensors. For finite-size systems, we identify a fundamental trade-off between robustness to uncertainty and the ability to retain a quantum advantage at the critical point. Our results contribute to a deeper understanding of the practical limitations of critical quantum metrology and provide a route toward its more resilient implementation.

quant-ph↗

arXiv2024

Nonequilibrium Nonlinear Effects and Dynamical Boson Condensation in a Driven-Dissipative Wannier-Stark Lattice

Driven-dissipative light-matter systems can exhibit collective nonequilibrium phenomena due to loss and gain processes on the one hand and effective photon-photon interactions on the other hand. As generic example we study a bosonic lattice system implemented via an array of driven-dissipative coupled nonlinear resonators with linearly increasing resonance frequencies across the lattice. The model also describes a driven-dissipative Bose-Hubbard model in a tilted potential without a particle-conservation constraint. We numerically predict a diverse range of stationary and non-stationary states resulting from the interplay of the tilt, tunneling, on-site interactions and loss and gain processes. Our key finding is that, under weak on-site interactions, the bosons mostly condense into a selected, single-particle Wannier-Stark state without exhibiting the expected Bloch oscillations. As the strength of the onsite interactions increase, a non-stationary regime emerges which, surprisingly, exhibits periodic Bloch-type oscillations. As a direct consequence of the driven-dissipative nature of the system we predict a highly nontrivial phase diagram including regular oscillating as well as chaotic dynamical regimes. While a straightforward photonic implementation using microwave or optical modes is possible, such dynamics might also be observable for an ultracold gas in a vertical lattice with gravity or a tilted external potential.

quant-ph↗

arXiv2024

Vacuum Rabi splitting as a manifestation of virtual two-mode squeezing: Extracting the squeezing parameters from frequency shifts

Vacuum Rabi splitting relies on symmetrical splitting of the common resonance frequency of atoms and the cavity in which the atoms reside. In this work, we argue that vacuum Rabi splitting is a manifestation of virtual light-matter two-mode squeezing. We establish a connection between squeezing parameters of virtual excitations and frequency shifts of the physical modes. To this end, we use the mapping between the Dicke model and two interacting harmonic oscillators, which we analyze in the framework of bare and physical modes. Finally, we suggest that such virtual squeezing of quantum fields might also play a role in quantum field theories.

quant-ph↗

arXiv2024

Temperature-Enhanced Critical Quantum Metrology

We show that the performance of critical quantum metrology protocols, counter-intuitively, can be enhanced by finite temperature. We consider a toy-model squeezing Hamiltonian, the Lipkin-Meshkov-Glick model and the paradigmatic Ising model. We show that the temperature enhancement of the quantum Fisher information can be achieved by adiabatic preparation of the critical state and by preparing it directly in the proximity of the critical point. We also find a relatively simple, however, non-optimal measurement capable of harnessing finite temperature to increase the parameter estimation sensitivity. Therefore, we argue that temperature can be considered as a resource in critical quantum metrology.

quant-ph↗

arXiv2024

Combining critical and quantum metrology

Critical metrology relies on the precise preparation of a system in its ground state near a quantum phase transition point where quantum correlations get very strong. Typically this increases the quantum Fisher information with respect to changes in system parameters and thus improves the optimally possible measurement precision limited by the Cramér-Rao bound. Hence critical metrology involves encoding information about the unknown parameter in changes of the system's ground state. Conversely, in conventional metrology methods like Ramsey interferometry, the eigenstates of the system remain unchanged, and information about the unknown parameter is encoded in the relative phases that excited system states accumulate during their time evolution. Here we introduce an approach combining these two methodologies into a unified protocol applicable to closed and driven-dissipative systems. We show that the quantum Fisher information in this case exhibits an additional interference term originating from the interplay between eigenstate and relative phase changes. We provide analytical expressions for the quantum and classical Fisher information in such a setup, elucidating as well a straightforward measurement approach that nearly attains the maximum precision permissible under the Cramér-Rao bound. We showcase these results by focusing on the squeezing Hamiltonian, which characterizes the thermodynamic limit of Dicke and Lipkin-Meshkov-Glick Hamiltonians.

quant-ph↗

arXiv2024

Unique Steady-State Squeezing in a Driven Quantum Rabi Model

Squeezing is essential to many quantum technologies and our understanding of quantum physics. Here we develop a theory of steady-state squeezing that can be generated in the closed and open quantum Rabi as well as Dicke model. To this end, we eliminate the spin dynamics which effectively leads to an abstract harmonic oscillator whose eigenstates are squeezed with respect to the physical harmonic oscillator. The generated form of squeezing has the unique property of time-independent uncertainties and squeezed dynamics, a novel type of quantum behavior. Such squeezing might find applications in continuous back-action evading measurements and should already be observable in optomechanical systems and Coulomb crystals.

quant-ph↗

arXiv2023

Squeezing of the quantum electromagnetic vacuum

It is commonly agreed that the electromagnetic vacuum is not empty but filled with virtual photons. This leads to effects like Lamb shift and spontaneous emission. Here we argue that if the vacuum has virtual photons it might mean that it is very weakly squeezed and therefore the electromagnetic field is not in its ground state (vacuum) but in an excited dark state. We suggest a stringent test relying on measuring various properties of the electromagnetic field to exclude this yet-untested squeezing hypothesis. This could be done by measuring the number of photons as a function of frequency and comparing it with the spectrum of electric (or magnetic) field fluctuations. If such squeezing exists, it might shed new light on cosmological phase transitions and give complementary information to the observed microwave background radiation as well as be a possible candidate for dark energy.

quant-ph↗

arXiv2022

Squeezing and overcoming the Heisenberg scaling with spin-orbit coupled quantum gases

We predict that exploiting spin-orbit coupling in a harmonically trapped spinor quantum gas can lead to scaling of the optimal measurement precision beyond the Heisenberg scaling. We show that quadratic scaling with the number of atoms can be facilitated via squeezed center-of-mass excitations of the atomic motion using a 1D spin-orbit coupled fermions or strongly interacting bosons (Tonks-Girardeau gas). Based on predictions derived from analytic calculations of the corresponding quantum Fisher information, we then introduce a protocol which overcomes the Heisenberg scaling (and limit) with help of a tailored excited and entangled many-body state of a non-interacting Bose-Einstein condensate. We identify corresponding optimal measurements and argue that even finite temperature as a source of decoherence is, in principle, rather favorable for the obtainable precision scaling.

quant-ph↗

arXiv2022

Distributed quantum sensing with optical lattices

In distributed quantum sensing the correlations between multiple modes, typically of a photonic system, are utilized to enhance the measurement precision of an unknown parameter. In this work we investigate the metrological potential of a multi-mode, tilted Bose-Hubbard system and show that it can allow for parameter estimation at the Heisenberg limit of $(N(M-1)T)^{2}$, where $N$ is the number of particles, $M$ is the number of modes, and $T$ is the measurement time. The quadratic dependence on the number of modes can be used to increase the precision compared to typical metrological systems with two atomic modes only, and does not require correlations between different modes. We show that the limit can be reached by using an optimized initial state given as the superposition of all the atoms occupying the first and the last site. Subsequently, we present strategies that would allow to obtain quadratic dependence on $M$ of the Fisher information in a more realistic experimental setup.

quant-ph↗

arXiv2022

Harnessing the center-of-mass excitations in quantum metrology

In quantum metrology, one typically creates correlations among atoms or photons to enhance measurement precision. Here, we show how one can use other excitations to perform quantum-enhanced measurements on the example of center-of-mass excitations of a spin-orbit coupled Bose-Einstein condensate and a Coulomb crystal. We also present a method to simulate a homodyne detection of center-of-mass excitations in these systems, which is required for optimal estimation.

quant-ph↗

arXiv2022

Understanding and Improving Critical Metrology. Quenching Superradiant Light-Matter Systems Beyond the Critical Point

We carefully examine critical metrology and present an improved critical quantum metrology protocol which relies on quenching a system exhibiting a superradiant quantum phase transition beyond its critical point. We show that this approach can lead to an exponential increase of the quantum Fisher information in time with respect to existing critical quantum metrology protocols relying on quenching close to the critical point and observing power law behaviour. We demonstrate that the Cramér-Rao bound can be saturated in our protocol through the standard homodyne detection scheme. We explicitly show its advantage using the archetypal setting of the Dicke model and explore a quantum gas coupled to a single-mode cavity field as a potential platform. In this case an additional exponential enhancement of the quantum Fisher information can in practice be observed with the number of atoms $N$ in the cavity, even in the absence of $N$-body coupling terms.

quant-ph↗

arXiv2022

Squeezing by Critical Speeding-up: Applications in Quantum Metrology

We present an alternative protocol allowing for the preparation of critical states that instead of suffering from the critical slowing-down benefits from the critical speeding-up. Paradoxically, we prepare these states by going away from the critical point which allows for the speed-up. We apply the protocol to the paradigmatic quantum Rabi model and its classical oscillator limit as well as the Lipkin-Meshkov-Glick model. Subsequently, we discuss the application of the adiabatic speed-up protocol in quantum metrology and compare its performance with critical quantum metrology. We show that critical quantum metrology with the Lipkin-Meshkov-Glick model cannot even overcome the standard quantum limit, and we argue that, even though critical metrology protocols can overcome it in some cases, critical metrology is a suboptimal metrological strategy. Finally, we conclude that systems exhibiting a phase transition are indeed interesting from the viewpoint of quantum technologies, however, it may not be the critical point that should attract the most attention.

quant-ph↗